Citation
Rice, John Rischard (1959) The characterization of best nonlinear Tchebycheff approximations. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd02102006083607
Abstract
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Consider a continuous function, F([...]) of n parameters and [...]. Such a function is said to have Property NS if the following theorem is valid for every continuous function, f(x):
THEOREM: F([...]) is a best approximation to f(x) if and only if there are n+1 distinct points, [...], such that [...].
Depending an the basic assumptions on F, several sets of necessary and sufficient conditions are given for F to have Property NS. These conditions involve unisolvence and related concepts. The definition of Property NS is generalized and necessary and sufficient conditions on F are given for F to have this generalized property. The latter theory includes most common nonlinear approximating functions.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1959 
Record Number:  CaltechETD:etd02102006083607 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd02102006083607 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  594 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  10 Feb 2006 
Last Modified:  26 Dec 2012 02:30 
Thesis Files

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